# solution

Refer to Example 8.4.

a. Apply the Kruskalâ€“Wallis test to determine if there is a difference in the distributions of oxygen content for the various distances to the mouth of the Mississippi River.

b. Does your conclusion differ from the conclusion reached in Exercise 8.16?

Example 8.4

Example 8.4

Marine biologists are studying a major reduction in the number of shrimp and commercial fish in the Gulf of Mexico. The area in which the Mississippi River enters the gulf is one of the areas of greatest concern. The biologists hypothesize that nutrient-rich water, including mainly nitrogens from the farmlands of the Midwest, flows into the gulf, which results in rapid growth in algae that feeds zooplankton. Bacteria then feed on the zooplankton pellets and dead algae, resulting in a depletion of the oxygen in the water. The more mobile marine life flees these regions, while the less mobile marine life dies from hypoxia. To monitor this condition, the mean dissolved oxygen contents (in ppm) of four areas at increasing distance from the mouth of the Mississippi were determined. A random sample of 10 water samples was taken at a depth of 12 meters in each of the four areas. The sample data are given in Table 8.16. The biologists want to test whether the mean oxygen content is lower in those areas closer to the mouth of the Mississippi.

a. Run a test of the equality of the population variances with a Â .05.

b. Transform the data if necessary to obtain a new data set in which the observations have equal variances.

Exercise 8.16

Refer to Example 8.4.

a. For the model yij Â Â Â ti Â eij, what are the values of , t1, t2, t3, and 4?

b. Using the observed data, provide estimates of , t1, t2, t3, and s with the constraint t4 Â 0.

Example 8.4

Marine biologists are studying a major reduction in the number of shrimp and commercial fish in the Gulf of Mexico. The area in which the Mississippi River enters the gulf is one of the areas of greatest concern. The biologists hypothesize that nutrient-rich water, including mainly nitrogens from the farmlands of the Midwest, flows into the gulf, which results in rapid growth in algae that feeds zooplankton. Bacteria then feed on the zooplankton pellets and dead algae, resulting in a depletion of the oxygen in the water. The more mobile marine life flees these regions, while the less mobile marine life dies from hypoxia. To monitor this condition, the mean dissolved oxygen contents (in ppm) of four areas at increasing distance from the mouth of the Mississippi were determined. A random sample of 10 water samples was taken at a depth of 12 meters in each of the four areas. The sample data are given in Table 8.16. The biologists want to test whether the mean oxygen content is lower in those areas closer to the mouth of the Mississippi.

a. Run a test of the equality of the population variances with a Â .05.

b. Transform the data if necessary to obtain a new data set in which the observations have equal variances.

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